Table of contents

1. Introduction to Accounting1h 21m
2. Transaction Analysis1h 13m
3. Accrual Accounting Concepts2h 38m
4. Merchandising Operations2h 30m
5. Inventory1h 55m
6. Internal Controls and Reporting Cash1h 16m
7. Receivables and Investments3h 8m
8. Long Lived Assets5h 1m
9. Current Liabilities2h 19m
10. Time Value of Money1h 23m
- Time Value of Money Equations
  35m
- Using Time Value of Money Tables
  47m
11. Long Term Liabilities2h 45m
12. Stockholders' Equity2h 15m
13. Statement of Cash Flows2h 24m
14. Financial Statement Analysis5h 25m
15. GAAP vs IFRS56m

10. Time Value of Money

Time Value of Money Equations

Financial Accounting

10. Time Value of Money

Time Value of Money Equations

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Multiple Choice

Which of the following formulas correctly calculates the future value of an ordinary annuity when additional equal investments are made at the end of each period for $n$ periods at an interest rate $r$ per period?

$FV = PMT \times \dfrac{1 - (1 + r)^{-n}}{r}$

$FV = PV \times (1 - r)^n$

$FV = PV \times (1 + r)^n$

$FV = PMT \times \dfrac{(1 + r)^n - 1}{r}$

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Verified step by step guidance

Step 1: Understand the concept of an ordinary annuity. An ordinary annuity involves equal payments (PMT) made at the end of each period for a specified number of periods ($n$) at a given interest rate ($r$). The future value (FV) represents the total value of these payments compounded at the interest rate.

Step 2: Recall the formula for the future value of an ordinary annuity. The correct formula is $FV = PMT \times \dfrac{(1 + r)^n - 1}{r}$. This formula accounts for the compounding effect of the interest rate on the periodic payments.

Step 3: Analyze why the other formulas provided are incorrect. For example: - $FV = PMT \times \dfrac{1 - (1 + r)^{-n}}{r}$ is incorrect because it represents the present value of an ordinary annuity, not the future value. - $FV = PV \times (1 - r)^n$ is incorrect because it does not account for compounding correctly. - $FV = PV \times (1 + r)^n$ is incorrect because it calculates the future value of a single lump sum, not an annuity.

Step 4: Break down the correct formula. The term $(1 + r)^n$ represents the compounding factor over $n$ periods, and subtracting 1 accounts for the accumulation of payments. Dividing by $r$ adjusts for the periodic interest rate applied to each payment.

Step 5: Apply the formula to calculate the future value of an ordinary annuity when given specific values for PMT, $r$, and $n$. Substitute the values into $FV = PMT \times \dfrac{(1 + r)^n - 1}{r}$ and simplify step by step to find the future value.